The multiplication of whole numbers (234) and (37) can be done using three methods: the basic algorithm, the partial sums method, and the distributive property, all yielding the final answer of 8658.
To multiply the whole numbers (234) and (37), we can use three methods: the basic method, the partial sums method, and using the distributive property.
Basic Method
We line up the numbers vertically and multiply each digit of the second number by each digit of the first number, remembering to add any carries as we go:
234
x 37
-----
1638 (234 x 7)
+ 702 (234 x 30, shift one position to the left)
-----
8658
Partial Sums Method
This involves breaking down each number into their place values and multiplying each separately:
-
- 200 x 30 = 6000
-
- 200 x 7 = 1400
-
- 30 x 30 = 900
-
- 30 x 7 = 210
-
- 4 x 30 = 120
-
- 4 x 7 = 28
Add those partial sums together to get the final answer:
6000 + 1400 + 900 + 210 + 120 + 28 = 8658.
Distributive Property
We use the idea that a(b + c) = ab + ac. Separate 37 into 30 + 7 and multiply each by 234:
234(30 + 7)
=234 x 30 + 234 x 7
=7020 + 1638
=8658
So, these methods provide a step-by-step explanation for multiplying whole numbers and lead to the same final answer of 8658.